First slide

Inductance

Question

In the circuit shown, X is joined to Y for a long time and then X is joined to Z. The total heat produced in R₂ is

Moderate

A

$\frac{{LE}^{2}}{2 R_{1}^{2}}$
B

$\frac{{LE}^{2}}{2 R_{2}^{2}}$
C

$\frac{{LE}^{2}}{2 R_{1} R_{2}}$
D

$\frac{{LE}^{2} R_{2}}{2 R_{1}^{3}}$

Solution

Steady-state current in $L = I_{0} = \frac{E}{R_{1}}$
Energy stored in L
$= \frac{1}{2} {LI}_{0}^{2} = \frac{1}{2} L (\frac{E^{2}}{R_{1}^{2}})$
= heat produced in R₂ during discharge.

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